Overheating can be caused by a number of different things. Common heat sources are engines while they are active, and aerodynamic heating. Different engines produce different levels of heat (which varies with the throttle used), and have different heat tolerances, resulting in some being more problematic than others. Heat flows to adjacent parts via conduction, so it is not always the part producing the heat which explodes, but a less heat tolerant part which is too close to it. Parts which are too close to, or directly in the path of, a rocket exhaust will gain heat and can overheat, and thrust vectoring or gimballing must be considered for that as well.

Practical overheat concerns

As of version 1.0.2[outdated], overheat only really matters if the overheat bar reaches 100%. If the bar fills up, the part explodes; if it doesn't fill up, there's no immediate problem.

In practice, this means that overheating can often be entirely ignored. For engines, the fuel supply is frequently exhausted long before it reaches 100%, or the burn is completed and the engine shutdown again.

It's frequently unnecessary to make changes to eliminate the overheat. One way to approach it is to simply ignore overheat entirely when designing, then try the craft on some normal flight profiles. If the overheat bars stay comfortably below 100% (e.g. no more than about 80%), it's not an issue. With the new thermal system added in 1.0, it has now become important to additionally factor in leaving sufficient unused overheat capacity if heat from a source other than the running engine is expected, such as re-entry aerodynamic heating, but the same philosophy works where staying below 100% is all that really matters.

Heating due to reentry

When parts travel through the atmosphere at high speeds, they will begin to heat up. Generally, the faster you go, the faster you heat up. This can be mitigated by ablative heat shields, introduced in version 1.0. Ablative heat shields use a resource called "Ablator." They protect parts stack attached above them by burning off (or ablating) ablator. A heat shield has far more ablator in it than is needed for a reentry from low Kerbin orbit, so one can remove some ablator to save weight when only reentering from low Kerbin orbit.

Internal heating mechanics

Since 1.0.2, all parts have heating values which can be shown by enabling "Display Thermal Data in Action Menus" underneath the Thermal tag of the Physics branch of the Debug Toolbar. When enabled, seven extra values will be shown in the action menus of each part (shown when a part is right-clicked). These are the numbers that influence how parts of a rocket heats up.

Thermal Mass

This number is how much heat it takes to heat up a part. For example, a part with a higher thermal mass will heat up slower than a part with lower thermal mass. This number is influenced by the size of the part, and, if the part is a fuel tank, the amount of fuel remaining in the tank. By default it is 800KJ/(tonne•kelvin)

Temp

Temp Ext

This is the temperature, in Kelvin, of the air or space surrounding that part.

Cond Flux

This is the speed that heat is conducting into or out of the selected part. Conduction is the spreading of heat through contact.
A positive number means that the part is gaining heat due to conduction, while a negative number means that it is losing heat.

Conv Flux

This is the speed that heat is convecting into or out of the selected part. Convection is the spreading of heat through the surrounding atmosphere. This number only applies in the atmosphere.
A positive number means that the part is gaining heat due to convection, while a negative number means that it is losing heat.

Rad Flux

This is the speed that heat is radiating into or out of the selected part. Radiation is the spreading of heat through the surrounding vacuum.
A positive number means that the part is gaining heat due to radiation, while a negative number means that it is losing heat.

Int Flux

This is the speed that the part is generating heat internally. This number usually only applies to engines and drills. This value is influenced by heat shields which consume ablator to absorb heat.